The Kennicutt-Schmidt law and the main sequence of galaxies in Newtonian and Milgromian dynamics

The Kennicutt-Schmidt law is an empirical relation between the star formation rate surface density (Σ_SFR) and the gas surface density (Σ_gas) in disc galaxies. The relation has a power-law form Σ_SFR ∝ Σ_gasⁿ. Assuming that star formation results from gravitational collapse of the interstellar medium, Σ_SFR can be determined by dividing Σ_gas by the local free-fall time t_ff. The formulation of t_ff yields the relation between Σ_SFR and Σ_gas, assuming that a constant fraction (Σ_SFE) of gas is converted into stars every t_ff. This is done here for the first time using Milgromian dynamics (MOND). Using linear stability analysis of a uniformly rotating thin disc, it is possible to determine the size of a collapsing perturbation within it. This lets us evaluate the sizes and masses of clouds (and their t_ff) as a function of Σ_gas and the rotation curve. We analytically derive the relation Σ_SFR ∝ Σ_gasⁿ both in Newtonian and Milgromian dynamics, finding that n = 1.4. The difference between the two cases is a change only to the constant pre-factor, resulting in increased Σ_SFR of up to 25 per cent using MOND in the central regions of dwarf galaxies. Due to the enhanced role of disc self-gravity, star formation extends out to larger galactocentric radii than in Newtonian gravity, with the clouds being larger. In MOND, a nearly exact representation of the present-day main sequence of galaxies is obtained if ϵ_SFE = constant ≈ 1.1 per cent. We also show that empirically found correction terms to the Kennicutt-Schmidt law are included in the here presented relations. Furthermore, we determine that if star formation is possible, then the temperature only affects Σ_SFR by at most a factor of √2.